

A231295


Number of (n+1) X (1+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..2 introduced in row major order.


1



1, 2, 4, 12, 32, 92, 264, 756, 2176, 6252, 17976, 51684, 148592, 427228, 1228328, 3531604, 10153824, 29193548, 83935256, 241324740, 693839952, 1994879932, 5735538696, 16490418228, 47412092736, 136315920428, 391925964280
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OFFSET

1,2


LINKS



FORMULA

Empirical: a(n) = 2*a(n1) + 3*a(n2)  4*a(n4).
Empirical g.f.: x*(1 + x)^2*(1  2*x) / ((1  x)*(1  x  4*x^2  4*x^3)).  Colin Barker, Sep 28 2018


EXAMPLE

Some solutions for n=4:
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..1....0..1....0..1....0..0....0..0....0..0....0..0....0..0
..0..1....1..1....1..1....1..1....1..1....0..0....1..1....1..1....0..0....0..0
..1..1....1..1....0..0....2..2....1..1....0..1....1..2....1..0....1..1....0..0
..1..1....1..1....0..0....2..2....1..1....1..1....2..2....0..0....1..1....0..0


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



